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Results for “QR factorization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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6 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

The use of the QR factorization in the partial realization problem

The use of the QR factorization of the Hankel matrix in solving the partial realization problem is analyzed. Straightforward use of the QR factorization results in a realization scheme that possesses all of the computational advantages of Rissanen's realization scheme. These latter properties are computational efficiency, recursiveness, use of limited computer memory, and the realization of a system triplet having a condensed structure. Moreover, this scheme is robust when the order of the system corresponds to the rank of the Hankel matrix. When this latter condition is violated, an approximate realization could be determined via the QR factorization. In this second scheme, the given Hankel matrix is approximated by a low-rank non-Hankel matrix. Furthermore, it is demonstrated that column pivoting might be incorporated in this second scheme. The results presented are derived for a single input/single output system, but this does not seem to be a restriction.

Verhaegen, M. H.↗
NASA NTRS1987

The minimal residual QR-factorization algorithm for reliably solving subset regression problems

A new algorithm to solve test subset regression problems is described, called the minimal residual QR factorization algorithm (MRQR). This scheme performs a QR factorization with a new column pivoting strategy. Basically, this strategy is based on the change in the residual of the least squares problem. Furthermore, it is demonstrated that this basic scheme might be extended in a numerically efficient way to combine the advantages of existing numerical procedures, such as the singular value decomposition, with those of more classical statistical procedures, such as stepwise regression. This extension is presented as an advisory expert system that guides the user in solving the subset regression problem. The advantages of the new procedure are highlighted by a numerical example.

Verhaegen, M. H.↗
NASA NTRS1991

QR Factorization In The Partial-Realization Problem

Report discusses use of QR factorization in solving partial-realization problem. Subject matter relevant to characterization of system, details of which hidden (a "blackbox"), on basis of relationship between its inputs and outputs. When realization process successful, system shown linear with known number of degrees of freedom and representable by mathematical model providing basis for prediction of outputs and design of controllers.

Verhaegen, M. H.↗
NASA NTRS1990

Downdating a time-varying square root information filter

A new method to efficiently downdate an estimate and covariance generated by a discrete time Square Root Information Filter (SRIF) is presented. The method combines the QR factor downdating algorithm of Gill and the decentralized SRIF algorithm of Bierman. Efficient removal of either measurements or a priori information is possible without loss of numerical integrity. Moreover, the method includes features for detecting potential numerical degradation. Performance on a 300 parameter system with 5800 data points shows that the method can be used in real time and hence is a promising tool for interactive data analysis. Additionally, updating a time-varying SRIF filter with either additional measurements or a priori information proceeds analogously.

Muellerschoen, Ronald J.↗
NASA NTRS1992

Multivariable frequency domain identification via 2-norm minimization

The author develops a computational approach to multivariable frequency domain identification, based on 2-norm minimization. In particular, a Gauss-Newton (GN) iteration is developed to minimize the 2-norm of the error between frequency domain data and a matrix fraction transfer function estimate. To improve the global performance of the optimization algorithm, the GN iteration is initialized using the solution to a particular sequentially reweighted least squares problem, denoted as the SK iteration. The least squares problems which arise from both the SK and GN iterations are shown to involve sparse matrices with identical block structure. A sparse matrix QR factorization method is developed to exploit the special block structure, and to efficiently compute the least squares solution. A numerical example involving the identification of a multiple-input multiple-output (MIMO) plant having 286 unknown parameters is given to illustrate the effectiveness of the algorithm.

Bayard, David S.↗
NASA NTRS1996

Interkinetic and migratory behavior of a cohort of neocortical neurons arising in the early embryonic murine cerebral wall

Neocortical neuronogenesis occurs in the pseudostratified ventricular epithelium (PVE) where nuclei of proliferative cells undergo interkinetic nuclear movement. A fraction of daughter cells exits the cell cycle as neurons (the quiescent, or Q, fraction), whereas a complementary fraction remains in the cell cycle (the proliferative, or P, fraction). By means of sequential thymidine and bromodeoxyuridine injections in mouse on embryonic day 14, we have monitored the proliferative and post-mitotic migratory behaviors of 1 and 2 hr cohorts of PVE cells defined by the injection protocols. Soon after mitosis, the Q fraction partitions into a rapidly exiting (up to 50 microns/hr) subpopulation (Qr) and a more slowly exiting (6 microns/hr) subpopulation (Qs). Qr and Qs are separated as two distributions on exit from the ventricular zone with an interpeak distance of approximately 40 microns. Cells in Qr and Qs migrate through the intermediate zone with no significant change in the interpeak distance, suggesting that they migrate at approximately the same velocities. The rate of migration increases with ascent through the intermediate zone (average 2-6.4 microns/hr) slowing only transiently on entry into the developing cortex. Within the cortex, Qr and Qs merge to form a single distribution most concentrated over layer V.

NASA Discipline Neuroscience↗